The base is done, I'll finish gluing the magnets on today or tomorrow, the coil core is in and I'll soon be cutting the wires and making the coil.
Then, though I know it's easy, I haven't ever made a circuit so I'm a bit anxious about it.
Looking at the photo of John's machine, I'm thinking of cutting a flat plastic lid or similar to attach the copper strips to - that the majority of the non-transistor parts are soldered too. Copper strips are not available locally, though I could probably get them if it's important, but I'm thinking of cutting open a copper tube, flattening it out and super gluing or hot gluing it to the plastic backing. Will that work? If so, is it better that the copper strips be thick (the walls of the tube are an 1/8" or so thick), or should I try to thin them out (I'd probably use a grinder and/or sander)?

The thicker metal could make it a little challenging to solder, but other than that you should be fine. Also i don't think a foot of wire one way or the other will keep you from a successful build.